CMOS-compatible light emitters are intensely investigated for integrated active silicon photonic circuits. One of the approaches to achieve on-chip light emitters is the epitaxial growth of Ge(Si) QDs on silicon. Their broad emission in the 1.3-1.5 um range is attractive for the telecom applications. We investigate optical properties of Ge(Si) QD multilayers, which are grown in a thin Si slab on an SOI wafer, by steady-state and time-resolved micro-photoluminescence. We identify Auger recombination as the governing mechanism of carrier dynamics in such heterostructures. Then we demonstrate the possibility of light manipulation at the nanoscale by resonant nanostructures investigating Si nanodisks with embedded Ge(Si) QDs. We show that the Mie resonances of the disks govern the enhancement of the photoluminescent signal from the embedded QDs due to a good spatial overlap of the emitter position with the electric field of Mie modes. Furthermore, we engineer collective Mie-resonances in a nanodisk trimer resulting in an increased Q-factor and an up to 10-fold enhancement of the luminescent signal due to the excitation of anti-symmetric magnetic and electric dipole modes. Using time-resolved measurements we show that the minima of the radiative lifetime coincide with the positions of the Mie resonances for a large variation of disk sizes confirming the impact of the Purcell effect on QD emission rate. Purcell factors at the different Mie-resonances are determined.